This chapter discusses the effects of disorder in fermionic systems, including Anderson localization. There are important differences for the disorder effects between the one-dimensional world, where localization occurs because electrons bump back and forth between impurities, and the higher dimensional world, where Anderson's localization is a rather subtle interference mechanism. The discussion looks at one-dimensional electrons subject to weak and dense impurities, in which the disorder can be replaced by its Gaussian limit. The application of disordered systems to quantum wires, one of the ultimate weapons to study individual one-dimensional systems, is considered.

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed

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Gen. cond-mat/9503074. 9] D. Cule. cond-mat/9505130. 10] Y.Y. Goldschmidt and B. Schaub, Nucl. Phys. B251 (1985) 77. 11] J. L. Cardy and S. Ostlund, Phys. Rev. B 25 (1982) 6899. 12] T. Giamarchi and P. Le Doussal. cond-mat/9409103. 13] See for example C. references therein. 14] R. Monasson. cond-mat/9503166. 15] R. Monasson and D. Lancaster, unpublished calculation. 16] D. Bernard and M. Bauer. cond-mat/9506141. 17] B. Coluzzi, D. J. Lancaster, E. Marinari and J. J. Ruiz-Lorenzo. Work in progress. 9 0.4 0.6 0.8 1.0 T-0.05 0 0.05 0.10 0.15 0.20 b 2 Figure 5: Coeecient of the log 2 (b 2) versus the temperature for diierent values of the parameter from a two parameter t. The same symbols as in gure 3. 4 Conclusions This comprehensive study reveals clear signals of a transition both in the static and dynamic properties of the system. The transition seems to occur at the same temperature whether determined by static or dynamic methods. The transition temperature does however depend on , being close to == only at small. We nd the general behavior predicted by RG arguments, that is: linear behavior of the dynamic exponent, z / , and quadratic behavior of the coeecient of log 2 , b 2 / 2. Detailed numerical agreement of the coeecients, especially in the case of the quadratic behavior, is lacking (by a factor of 14) while in the dynamic case the agreement is reasonable. Finally, an explanation of the dependence of all the quantities measured is needed. The essential diierence of opinion on the low temperature phase is between analyses based on the RG that predict a log 2 form for the correlator, and analysis based on a varia-tional approach that yield a log. The RG approach has been criticised because the solutions are unstable with respect to breaking of replica symmetry 12], however the signiicance of this is not clear since the techniques for dealing with replicas are not suuciently developed to deal eeectively with non mean eld situations. On the other hand, the variational approach has only been calculated for a gaussian ansatz which corresponds to leading order in some 1=N expansion. Recent results 16] using RG arguments for an N-component version of the Random Phase Sine Gordon model are interesting in that they calculate the coeecient of the log 2 term to be order 1=N 3. We hope that further analytic work in both approaches to understand the smallness of the log 2 coeecient seen in this and all other simulations, will lead to a resolution of the puzzle. Finally we believe that we have shown that it is possible obtain reliable and accurate numerical data for this rather contentious subject that can be extended and used to further 8 0.4 0.6 0.8 1.0 T 0 0.2 0.4 0.6 0.8 1.0 b 1 Figure 4: Coeecient of the log (b 1) versus the temperature for diierent values of the parameter from a two parameter t. The same symbols as in gure 3. The error bars are smaller that the size of the points. jack-knife. Figures 4 and 5 show the resulting values of the coeecients for = 0:5 and 2:0, and also the data for = 1 from reference 8]. T...

We have studied the motion of a magnetic domain wall (MDW) driven by a magnetic field H in a 2D ultrathin Pt͞Co͞Pt film showing perpendicular anisotropy and quenched disorder. MDW velocity measurements down to the so called creep regime show that the average energy barrier scales as ͑1͞H͒ m with m 0.24 6 0.04 and that the correlation function along a MDW is governed by a wandering exponent z 0.69 6 0.07, in very good agreement with theories giving m 0.25 and z 2͞3. This is the first direct measurement of the creep regime for a moving interface in a disordered medium. [S0031-9007(97)

The Bose–Einstein condensate (BEC) is a fascinating state of matter predicted to occur for particles obeying Bose statistics. Although the BEC has been observed with bosonic atoms in liquid helium and cold gases, the concept is much more general. We here review analogous states, where excitations in magnetic insulators form the BEC. In antiferromagnets, elementary excitations are magnons, quasiparticles with integer spin and Bose statistics. In certain experiments their density can be controlled by an applied magnetic field leading to the formation of a BEC. Furthermore, interactions between the excitations and the interplay with the crystalline lattice produce very rich physics compared with the canonical BEC. Studies of magnon condensation in a growing number of magnetic materials thus provide a unique window into an exciting world of quantum phase transitions and exotic quantum states, with striking parallels to phenomena studied in ultracold atomic gases in optical lattices

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to O(ǫ = 4 − d), the functional renormalization group. We find universal logarithmic growth of displacements for 2 < d < 4: u(x) − u(0) 2 ∼ A d log |x| and persistence of algebraic quasi-long range translational order. When the two methods can be compared they agree within 10% on the value of A d . We compute the function describing the crossover between the "random manifold" regime and the logarithmic regime. This crossover should be observable in present decoration experiments. 74.60.Ge, 05.20.-y Typeset using REVT E X